/*
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef _SYS_TREE_H_
#define _SYS_TREE_H_

/*
 * This file defines data structures for different types of trees:
 * splay trees and red-black trees.
 *
 * A splay tree is a self-organizing data structure.  Every operation
 * on the tree causes a splay to happen.  The splay moves the requested
 * node to the root of the tree and partly rebalances it.
 *
 * This has the benefit that request locality causes faster lookups as
 * the requested nodes move to the top of the tree.  On the other hand,
 * every lookup causes memory writes.
 *
 * The Balance Theorem bounds the total access time for m operations
 * and n inserts on an initially empty tree as O((m + n)lg n).  The
 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
 *
 * A red-black tree is a binary search tree with the node color as an
 * extra attribute.  It fulfills a set of conditions:
 *  - every search path from the root to a leaf consists of the
 *    same number of black nodes,
 *  - each red node (except for the root) has a black parent,
 *  - each leaf node is black.
 *
 * Every operation on a red-black tree is bounded as O(lg n).
 * The maximum height of a red-black tree is 2lg (n+1).
 */

#define SPLAY_HEAD(name, type)            \
struct name {               \
  struct type *sph_root; /* root of the tree */     \
}

#define SPLAY_INITIALIZER(root)           \
  { NULL }

#define SPLAY_INIT(root) do {           \
  (root)->sph_root = NULL;          \
} while (0)

#define SPLAY_ENTRY(type)           \
struct {                \
  struct type *spe_left; /* left element */     \
  struct type *spe_right; /* right element */     \
}

#define SPLAY_LEFT(elm, field)    (elm)->field.spe_left
#define SPLAY_RIGHT(elm, field)   (elm)->field.spe_right
#define SPLAY_ROOT(head)    (head)->sph_root
#define SPLAY_EMPTY(head)   (SPLAY_ROOT(head) == NULL)

/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
#define SPLAY_ROTATE_RIGHT(head, tmp, field) do {     \
  SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  SPLAY_RIGHT(tmp, field) = (head)->sph_root;     \
  (head)->sph_root = tmp;           \
} while (0)

#define SPLAY_ROTATE_LEFT(head, tmp, field) do {      \
  SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  SPLAY_LEFT(tmp, field) = (head)->sph_root;      \
  (head)->sph_root = tmp;           \
} while (0)

#define SPLAY_LINKLEFT(head, tmp, field) do {       \
  SPLAY_LEFT(tmp, field) = (head)->sph_root;      \
  tmp = (head)->sph_root;           \
  (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);   \
} while (0)

#define SPLAY_LINKRIGHT(head, tmp, field) do {        \
  SPLAY_RIGHT(tmp, field) = (head)->sph_root;     \
  tmp = (head)->sph_root;           \
  (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);  \
} while (0)

#define SPLAY_ASSEMBLE(head, node, left, right, field) do {   \
  SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
  SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
  SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
  SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
} while (0)

/* Generates prototypes and inline functions */

#define SPLAY_PROTOTYPE(name, type, field, cmp)       \
void name##_SPLAY(struct name *, struct type *);      \
void name##_SPLAY_MINMAX(struct name *, int);       \
struct type *name##_SPLAY_INSERT(struct name *, struct type *);   \
struct type *name##_SPLAY_REMOVE(struct name *, struct type *);   \
                  \
/* Finds the node with the same key as elm */       \
static __inline struct type *           \
name##_SPLAY_FIND(struct name *head, struct type *elm)      \
{                 \
  if (SPLAY_EMPTY(head))            \
    return(NULL);           \
  name##_SPLAY(head, elm);          \
  if ((cmp)(elm, (head)->sph_root) == 0)        \
    return (head->sph_root);        \
  return (NULL);              \
}                 \
                  \
static __inline struct type *           \
name##_SPLAY_NEXT(struct name *head, struct type *elm)      \
{                 \
  name##_SPLAY(head, elm);          \
  if (SPLAY_RIGHT(elm, field) != NULL) {        \
    elm = SPLAY_RIGHT(elm, field);        \
    while (SPLAY_LEFT(elm, field) != NULL) {    \
      elm = SPLAY_LEFT(elm, field);     \
    }             \
  } else                \
    elm = NULL;           \
  return (elm);             \
}                 \
                  \
static __inline struct type *           \
name##_SPLAY_MIN_MAX(struct name *head, int val)      \
{                 \
  name##_SPLAY_MINMAX(head, val);         \
        return (SPLAY_ROOT(head));          \
}

/* Main splay operation.
 * Moves node close to the key of elm to top
 */
#define SPLAY_GENERATE(name, type, field, cmp)        \
struct type *               \
name##_SPLAY_INSERT(struct name *head, struct type *elm)    \
{                 \
    if (SPLAY_EMPTY(head)) {            \
      SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;  \
    } else {                \
      int __comp;             \
      name##_SPLAY(head, elm);          \
      __comp = (cmp)(elm, (head)->sph_root);      \
      if(__comp < 0) {            \
        SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
        SPLAY_RIGHT(elm, field) = (head)->sph_root;   \
        SPLAY_LEFT((head)->sph_root, field) = NULL;   \
      } else if (__comp > 0) {          \
        SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
        SPLAY_LEFT(elm, field) = (head)->sph_root;    \
        SPLAY_RIGHT((head)->sph_root, field) = NULL;  \
      } else              \
        return ((head)->sph_root);        \
    }                 \
    (head)->sph_root = (elm);           \
    return (NULL);              \
}                 \
                  \
struct type *               \
name##_SPLAY_REMOVE(struct name *head, struct type *elm)    \
{                 \
  struct type *__tmp;           \
  if (SPLAY_EMPTY(head))            \
    return (NULL);            \
  name##_SPLAY(head, elm);          \
  if ((cmp)(elm, (head)->sph_root) == 0) {      \
    if (SPLAY_LEFT((head)->sph_root, field) == NULL) {  \
      (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
    } else {            \
      __tmp = SPLAY_RIGHT((head)->sph_root, field); \
      (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
      name##_SPLAY(head, elm);      \
      SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
    }             \
    return (elm);           \
  }               \
  return (NULL);              \
}                 \
                  \
void                  \
name##_SPLAY(struct name *head, struct type *elm)     \
{                 \
  struct type __node, *__left, *__right, *__tmp;      \
  int __comp;             \
\
  SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
  __left = __right = &__node;         \
\
  while ((__comp = (cmp)(elm, (head)->sph_root))) {   \
    if (__comp < 0) {         \
      __tmp = SPLAY_LEFT((head)->sph_root, field);  \
      if (__tmp == NULL)        \
        break;          \
      if ((cmp)(elm, __tmp) < 0){     \
        SPLAY_ROTATE_RIGHT(head, __tmp, field); \
        if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
          break;        \
      }           \
      SPLAY_LINKLEFT(head, __right, field);   \
    } else if (__comp > 0) {        \
      __tmp = SPLAY_RIGHT((head)->sph_root, field); \
      if (__tmp == NULL)        \
        break;          \
      if ((cmp)(elm, __tmp) > 0){     \
        SPLAY_ROTATE_LEFT(head, __tmp, field);  \
        if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
          break;        \
      }           \
      SPLAY_LINKRIGHT(head, __left, field);   \
    }             \
  }               \
  SPLAY_ASSEMBLE(head, &__node, __left, __right, field);    \
}                 \
                  \
/* Splay with either the minimum or the maximum element     \
 * Used to find minimum or maximum element in tree.     \
 */                 \
void name##_SPLAY_MINMAX(struct name *head, int __comp) \
{                 \
  struct type __node, *__left, *__right, *__tmp;      \
\
  SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
  __left = __right = &__node;         \
\
  while (1) {             \
    if (__comp < 0) {         \
      __tmp = SPLAY_LEFT((head)->sph_root, field);  \
      if (__tmp == NULL)        \
        break;          \
      if (__comp < 0){        \
        SPLAY_ROTATE_RIGHT(head, __tmp, field); \
        if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
          break;        \
      }           \
      SPLAY_LINKLEFT(head, __right, field);   \
    } else if (__comp > 0) {        \
      __tmp = SPLAY_RIGHT((head)->sph_root, field); \
      if (__tmp == NULL)        \
        break;          \
      if (__comp > 0) {       \
        SPLAY_ROTATE_LEFT(head, __tmp, field);  \
        if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
          break;        \
      }           \
      SPLAY_LINKRIGHT(head, __left, field);   \
    }             \
  }               \
  SPLAY_ASSEMBLE(head, &__node, __left, __right, field);    \
}

#define SPLAY_NEGINF  -1
#define SPLAY_INF 1

#define SPLAY_INSERT(name, x, y)  name##_SPLAY_INSERT(x, y)
#define SPLAY_REMOVE(name, x, y)  name##_SPLAY_REMOVE(x, y)
#define SPLAY_FIND(name, x, y)    name##_SPLAY_FIND(x, y)
#define SPLAY_NEXT(name, x, y)    name##_SPLAY_NEXT(x, y)
#define SPLAY_MIN(name, x)    (SPLAY_EMPTY(x) ? NULL  \
          : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
#define SPLAY_MAX(name, x)    (SPLAY_EMPTY(x) ? NULL  \
          : name##_SPLAY_MIN_MAX(x, SPLAY_INF))

#define SPLAY_FOREACH(x, name, head)          \
  for ((x) = SPLAY_MIN(name, head);       \
       (x) != NULL;           \
       (x) = SPLAY_NEXT(name, head, x))

/* Macros that define a red-back tree */
#define RB_HEAD(name, type)           \
struct name {               \
  struct type *rbh_root; /* root of the tree */     \
}

#define RB_INITIALIZER(root)            \
  { NULL }

#define RB_INIT(root) do {            \
  (root)->rbh_root = NULL;          \
} while (0)

#define RB_BLACK  0
#define RB_RED    1
#define RB_ENTRY(type)              \
struct {                \
  struct type *rbe_left;    /* left element */    \
  struct type *rbe_right;   /* right element */   \
  struct type *rbe_parent;  /* parent element */    \
  int rbe_color;      /* node color */    \
}

#define RB_LEFT(elm, field)   (elm)->field.rbe_left
#define RB_RIGHT(elm, field)    (elm)->field.rbe_right
#define RB_PARENT(elm, field)   (elm)->field.rbe_parent
#define RB_COLOR(elm, field)    (elm)->field.rbe_color
#define RB_ROOT(head)     (head)->rbh_root
#define RB_EMPTY(head)      (RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field) do {         \
  RB_PARENT(elm, field) = parent;         \
  RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;    \
  RB_COLOR(elm, field) = RB_RED;          \
} while (0)

#define RB_SET_BLACKRED(black, red, field) do {       \
  RB_COLOR(black, field) = RB_BLACK;        \
  RB_COLOR(red, field) = RB_RED;          \
} while (0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x)
#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field) do {      \
  (tmp) = RB_RIGHT(elm, field);         \
  if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {   \
    RB_PARENT(RB_LEFT(tmp, field), field) = (elm);    \
  }               \
  RB_AUGMENT(elm);            \
  if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {    \
    if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
      RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
    else              \
      RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
  } else                \
    (head)->rbh_root = (tmp);       \
  RB_LEFT(tmp, field) = (elm);          \
  RB_PARENT(elm, field) = (tmp);          \
  RB_AUGMENT(tmp);            \
  if ((RB_PARENT(tmp, field)))          \
    RB_AUGMENT(RB_PARENT(tmp, field));      \
} while (0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {     \
  (tmp) = RB_LEFT(elm, field);          \
  if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {   \
    RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);   \
  }               \
  RB_AUGMENT(elm);            \
  if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {    \
    if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
      RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
    else              \
      RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
  } else                \
    (head)->rbh_root = (tmp);       \
  RB_RIGHT(tmp, field) = (elm);         \
  RB_PARENT(elm, field) = (tmp);          \
  RB_AUGMENT(tmp);            \
  if ((RB_PARENT(tmp, field)))          \
    RB_AUGMENT(RB_PARENT(tmp, field));      \
} while (0)

/* Generates prototypes and inline functions */
#define RB_PROTOTYPE(name, type, field, cmp)        \
void name##_RB_INSERT_COLOR(struct name *, struct type *);  \
void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
struct type *name##_RB_REMOVE(struct name *, struct type *);    \
struct type *name##_RB_INSERT(struct name *, struct type *);    \
struct type *name##_RB_FIND(struct name *, struct type *);    \
struct type *name##_RB_NEXT(struct type *);       \
struct type *name##_RB_MINMAX(struct name *, int);      \
                  \
 
/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define RB_GENERATE(name, type, field, cmp)       \
void                  \
name##_RB_INSERT_COLOR(struct name *head, struct type *elm)   \
{                 \
  struct type *parent, *gparent, *tmp;        \
  while ((parent = RB_PARENT(elm, field)) &&      \
      RB_COLOR(parent, field) == RB_RED) {      \
    gparent = RB_PARENT(parent, field);     \
    if (parent == RB_LEFT(gparent, field)) {    \
      tmp = RB_RIGHT(gparent, field);     \
      if (tmp && RB_COLOR(tmp, field) == RB_RED) {  \
        RB_COLOR(tmp, field) = RB_BLACK;  \
        RB_SET_BLACKRED(parent, gparent, field);\
        elm = gparent;        \
        continue;       \
      }           \
      if (RB_RIGHT(parent, field) == elm) {   \
        RB_ROTATE_LEFT(head, parent, tmp, field);\
        tmp = parent;       \
        parent = elm;       \
        elm = tmp;        \
      }           \
      RB_SET_BLACKRED(parent, gparent, field);  \
      RB_ROTATE_RIGHT(head, gparent, tmp, field); \
    } else {            \
      tmp = RB_LEFT(gparent, field);      \
      if (tmp && RB_COLOR(tmp, field) == RB_RED) {  \
        RB_COLOR(tmp, field) = RB_BLACK;  \
        RB_SET_BLACKRED(parent, gparent, field);\
        elm = gparent;        \
        continue;       \
      }           \
      if (RB_LEFT(parent, field) == elm) {    \
        RB_ROTATE_RIGHT(head, parent, tmp, field);\
        tmp = parent;       \
        parent = elm;       \
        elm = tmp;        \
      }           \
      RB_SET_BLACKRED(parent, gparent, field);  \
      RB_ROTATE_LEFT(head, gparent, tmp, field);  \
    }             \
  }               \
  RB_COLOR(head->rbh_root, field) = RB_BLACK;     \
}                 \
                  \
void                  \
name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
{                 \
  struct type *tmp;           \
  while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
      elm != RB_ROOT(head)) {         \
    if (RB_LEFT(parent, field) == elm) {      \
      tmp = RB_RIGHT(parent, field);      \
      if (RB_COLOR(tmp, field) == RB_RED) {   \
        RB_SET_BLACKRED(tmp, parent, field);  \
        RB_ROTATE_LEFT(head, parent, tmp, field);\
        tmp = RB_RIGHT(parent, field);    \
      }           \
      if ((RB_LEFT(tmp, field) == NULL ||   \
          RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
          (RB_RIGHT(tmp, field) == NULL ||    \
          RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
        RB_COLOR(tmp, field) = RB_RED;    \
        elm = parent;       \
        parent = RB_PARENT(elm, field);   \
      } else {          \
        if (RB_RIGHT(tmp, field) == NULL || \
            RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
          struct type *oleft;   \
          if ((oleft = RB_LEFT(tmp, field)))\
            RB_COLOR(oleft, field) = RB_BLACK;\
          RB_COLOR(tmp, field) = RB_RED;  \
          RB_ROTATE_RIGHT(head, tmp, oleft, field);\
          tmp = RB_RIGHT(parent, field);  \
        }         \
        RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
        RB_COLOR(parent, field) = RB_BLACK; \
        if (RB_RIGHT(tmp, field))   \
          RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
        RB_ROTATE_LEFT(head, parent, tmp, field);\
        elm = RB_ROOT(head);      \
        break;          \
      }           \
    } else {            \
      tmp = RB_LEFT(parent, field);     \
      if (RB_COLOR(tmp, field) == RB_RED) {   \
        RB_SET_BLACKRED(tmp, parent, field);  \
        RB_ROTATE_RIGHT(head, parent, tmp, field);\
        tmp = RB_LEFT(parent, field);   \
      }           \
      if ((RB_LEFT(tmp, field) == NULL ||   \
          RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
          (RB_RIGHT(tmp, field) == NULL ||    \
          RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
        RB_COLOR(tmp, field) = RB_RED;    \
        elm = parent;       \
        parent = RB_PARENT(elm, field);   \
      } else {          \
        if (RB_LEFT(tmp, field) == NULL ||  \
            RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
          struct type *oright;    \
          if ((oright = RB_RIGHT(tmp, field)))\
            RB_COLOR(oright, field) = RB_BLACK;\
          RB_COLOR(tmp, field) = RB_RED;  \
          RB_ROTATE_LEFT(head, tmp, oright, field);\
          tmp = RB_LEFT(parent, field); \
        }         \
        RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
        RB_COLOR(parent, field) = RB_BLACK; \
        if (RB_LEFT(tmp, field))    \
          RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
        RB_ROTATE_RIGHT(head, parent, tmp, field);\
        elm = RB_ROOT(head);      \
        break;          \
      }           \
    }             \
  }               \
  if (elm)              \
    RB_COLOR(elm, field) = RB_BLACK;      \
}                 \
                  \
struct type *               \
name##_RB_REMOVE(struct name *head, struct type *elm)     \
{                 \
  struct type *child, *parent, *old = elm;      \
  int color;              \
  if (RB_LEFT(elm, field) == NULL)        \
    child = RB_RIGHT(elm, field);       \
  else if (RB_RIGHT(elm, field) == NULL)        \
    child = RB_LEFT(elm, field);        \
  else {                \
    struct type *left;          \
    elm = RB_RIGHT(elm, field);       \
    while ((left = RB_LEFT(elm, field)))      \
      elm = left;         \
    child = RB_RIGHT(elm, field);       \
    parent = RB_PARENT(elm, field);       \
    color = RB_COLOR(elm, field);       \
    if (child)            \
      RB_PARENT(child, field) = parent;   \
    if (parent) {           \
      if (RB_LEFT(parent, field) == elm)    \
        RB_LEFT(parent, field) = child;   \
      else            \
        RB_RIGHT(parent, field) = child;  \
      RB_AUGMENT(parent);       \
    } else              \
      RB_ROOT(head) = child;        \
    if (RB_PARENT(elm, field) == old)     \
      parent = elm;         \
    (elm)->field = (old)->field;        \
    if (RB_PARENT(old, field)) {        \
      if (RB_LEFT(RB_PARENT(old, field), field) == old)\
        RB_LEFT(RB_PARENT(old, field), field) = elm;\
      else            \
        RB_RIGHT(RB_PARENT(old, field), field) = elm;\
      RB_AUGMENT(RB_PARENT(old, field));    \
    } else              \
      RB_ROOT(head) = elm;        \
    RB_PARENT(RB_LEFT(old, field), field) = elm;    \
    if (RB_RIGHT(old, field))       \
      RB_PARENT(RB_RIGHT(old, field), field) = elm; \
    if (parent) {           \
      left = parent;          \
      do {            \
        RB_AUGMENT(left);     \
      } while ((left = RB_PARENT(left, field)));  \
    }             \
    goto color;           \
  }               \
  parent = RB_PARENT(elm, field);         \
  color = RB_COLOR(elm, field);         \
  if (child)              \
    RB_PARENT(child, field) = parent;     \
  if (parent) {             \
    if (RB_LEFT(parent, field) == elm)      \
      RB_LEFT(parent, field) = child;     \
    else              \
      RB_RIGHT(parent, field) = child;    \
    RB_AUGMENT(parent);         \
  } else                \
    RB_ROOT(head) = child;          \
color:                  \
  if (color == RB_BLACK)            \
    name##_RB_REMOVE_COLOR(head, parent, child);    \
  return (old);             \
}                 \
                  \
/* Inserts a node into the RB tree */         \
struct type *               \
name##_RB_INSERT(struct name *head, struct type *elm)     \
{                 \
  struct type *tmp;           \
  struct type *parent = NULL;         \
  int comp = 0;             \
  tmp = RB_ROOT(head);            \
  while (tmp) {             \
    parent = tmp;           \
    comp = (cmp)(elm, parent);        \
    if (comp < 0)           \
      tmp = RB_LEFT(tmp, field);      \
    else if (comp > 0)          \
      tmp = RB_RIGHT(tmp, field);     \
    else              \
      return (tmp);         \
  }               \
  RB_SET(elm, parent, field);         \
  if (parent != NULL) {           \
    if (comp < 0)           \
      RB_LEFT(parent, field) = elm;     \
    else              \
      RB_RIGHT(parent, field) = elm;      \
    RB_AUGMENT(parent);         \
  } else                \
  {                                                                     \
    RB_ROOT(head) = elm;          \
  }                                                                     \
  name##_RB_INSERT_COLOR(head, elm);        \
  return (NULL);              \
}                 \
                  \
/* Finds the node with the same key as elm */       \
struct type *               \
name##_RB_FIND(struct name *head, struct type *elm)     \
{                 \
  struct type *tmp = RB_ROOT(head);       \
  int comp;             \
  while (tmp) {             \
    comp = cmp(elm, tmp);         \
    if (comp < 0)           \
      tmp = RB_LEFT(tmp, field);      \
    else if (comp > 0)          \
      tmp = RB_RIGHT(tmp, field);     \
    else              \
      return (tmp);         \
  }               \
  return (NULL);              \
}                 \
                  \
struct type *               \
name##_RB_NEXT(struct type *elm)          \
{                 \
  if (RB_RIGHT(elm, field)) {         \
    elm = RB_RIGHT(elm, field);       \
    while (RB_LEFT(elm, field))       \
      elm = RB_LEFT(elm, field);      \
  } else {              \
    if (RB_PARENT(elm, field) &&        \
        (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
      elm = RB_PARENT(elm, field);      \
    else {              \
      while (RB_PARENT(elm, field) &&     \
          (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
        elm = RB_PARENT(elm, field);    \
      elm = RB_PARENT(elm, field);      \
    }             \
  }               \
  return (elm);             \
}                 \
                  \
struct type *               \
name##_RB_MINMAX(struct name *head, int val)        \
{                 \
  struct type *tmp = RB_ROOT(head);       \
  struct type *parent = NULL;         \
  while (tmp) {             \
    parent = tmp;           \
    if (val < 0)            \
      tmp = RB_LEFT(tmp, field);      \
    else              \
      tmp = RB_RIGHT(tmp, field);     \
  }               \
  return (parent);            \
}

#define RB_NEGINF -1
#define RB_INF  1

#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y) name##_RB_FIND(x, y)
#define RB_NEXT(name, x, y) name##_RB_NEXT(y)
#define RB_MIN(name, x)   name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x)   name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head)         \
  for ((x) = RB_MIN(name, head);          \
       (x) != NULL;           \
       (x) = name##_RB_NEXT(x))

#endif  /* _SYS_TREE_H_ */
